Pith Number

pith:KJRV6YRV

pith:2007:KJRV6YRVKWWIQ5LRPJ7HFDO7M4

not attested not anchored not stored refs pending

The Witten equation and its virtual fundamental cycle

Huijun Fan, Tyler J. Jarvis, Yongbin Ruan

arxiv:0712.4025 v3 · 2007-12-24 · math.AG · hep-th · math-ph · math.AP · math.MP · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KJRV6YRVKWWIQ5LRPJ7HFDO7M4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:24:06.520489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52635f623555ac8875717a7e728ddf6736ae1917719bc6896c4137378de2dac1

Aliases

arxiv: 0712.4025 · arxiv_version: 0712.4025v3 · doi: 10.48550/arxiv.0712.4025 · pith_short_12: KJRV6YRVKWWI · pith_short_16: KJRV6YRVKWWIQ5LR · pith_short_8: KJRV6YRV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KJRV6YRVKWWIQ5LRPJ7HFDO7M4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 52635f623555ac8875717a7e728ddf6736ae1917719bc6896c4137378de2dac1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e16d47e4617bcd51f1565364f35ed82ece64976c9141c06779e16569fbc854c0",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.AP",
      "math.MP",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-12-24T20:07:52Z",
    "title_canon_sha256": "b0747acbceb627db188adfafa6146d4c96716b38439fed37b1fe7e400c8ce5c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.4025",
    "kind": "arxiv",
    "version": 3
  }
}